I tried simplifying the logarithm, I tried adding ln(y) to the other side (and negatizing, to subtract ln(x) and y from both sides), and a whole lot of other stuff. Nothing seems to work. Do you have any ideas?
I originally found this equation from the function f(x) = xe^x, and then I realised that inversing that function would let me solve a lot of problems I had unsolved (such as x^n = n^-x) that are otherwise seemingly impossible to solve. This is the farthest I got. I suppose you could please the algebra professors of the world and start from x = ye^y, but I'm not convinced that that's an efficient solution.
All help is appreciated! Google, wikipedia, and ChatGPT3 were no help, and I don't think anybody's asked this before.